ANSWER:
[tex]y=-\frac{5}{8}x-\frac{63}{8}[/tex]STEP-BY-STEP EXPLANATION:
We have the equation of the following line:
[tex]\begin{gathered} 5y−8x=−8 \\ \\ \text{ We solve for and to determine the slope:} \\ \\ 5y=-8+8x \\ \\ y=-\frac{8}{5}+\frac{8}{5}x \\ \\ y=\frac{8}{5}x-\frac{8}{5}\rightarrow y=mx+b \\ \\ \text{ therefore:} \\ \\ m=\frac{8}{5} \end{gathered}[/tex]We have that when two lines are perpendicular, the product of their slopes is equal to -1, in this way we calculate the slope of the desired line:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ \\ \text{ we replacing} \\ \\ \frac{8}{5}\cdot m_2=-1 \\ \\ m_2=-\frac{5}{8} \end{gathered}[/tex]Now with the slope and the point (1/5, −8), we calculate the y-intercept to later determine the equation of the line just like this:
[tex]\begin{gathered} -8=-\frac{5}{8}\cdot\frac{1}{5}+b \\ \\ -8=-\frac{1}{8}+b \\ \\ b=-8+\frac{1}{8} \\ \\ b=-\frac{63}{8} \\ \\ \text{ The equation would be:} \\ \\ y=-\frac{5}{8}x-\frac{63}{8} \end{gathered}[/tex]